Rates of spontaneous mutation vary greatly among organisms and among genes. We have previously described mutation rates that are characteristic of certain broad groups of organisms. (1) A new description of the mutation process has now been found for simple RNA viruses (riboviruses). When applied to published mutation frequencies, we find a central value of about 0.76 per genome replication. As a result of this high rate, riboviruses have nearly maximum sustainable mutation rates, and very small increases lead to extinction. (2) The characteristic mutation rate for DNA-based microbes is 0.0034 per genome replication. The question arises whether this rate is also to be found in extremophiles, and specifically in Archeons. We are gathering information about the mutation process in the Archeon Sulfolobus acidocaldarius growing at pH 3.5 at 75?C, in order to determine the mutation rate accurately and to characterize the kinds of mutations that arise spontaneously.